phenomenon

quantum phase transition

A phase transition occurring at absolute zero temperature, driven by quantum fluctuations.
18 related articles · 2 formulas

Description

A quantum phase transition is a phase transition that occurs at absolute zero temperature, driven not by thermal fluctuations but by quantum fluctuations. Unlike classical phase transitions (like water freezing), which are driven by temperature, quantum phase transitions are driven by changes in a non-thermal parameter such as pressure, magnetic field, or chemical composition. At the transition point, the ground state of the system changes dramatically, leading to new phases of matter with exotic properties.

History

The concept was developed in the 1970s and 1980s, with pioneering work by John Hertz, Subir Sachdev, and others. It has been extensively studied in condensed matter physics, particularly in heavy-fermion compounds and high-temperature superconductors.

How it works

In a quantum system, the ground state is determined by the competition between different terms in the Hamiltonian (e.g., kinetic energy vs. interaction energy). As an external parameter is tuned, the balance shifts, and at a critical value, the ground state undergoes a qualitative change. Near this quantum critical point, quantum fluctuations dominate, leading to universal behavior that can be described by quantum field theory. These fluctuations can also influence the system at finite temperatures, creating a 'quantum critical region' where unusual properties persist.

In practice

Quantum phase transitions are key to understanding high-temperature superconductivity, novel magnetic states, and the design of quantum materials. They also play a role in quantum computing, where controlling quantum fluctuations is essential.

Fun fact

Some quantum phase transitions are believed to be 'deconfined,' where the transition is not between two different phases but involves the fractionalization of particles into new quasiparticles, a phenomenon not seen in classical physics.

Concept graph →

Formulas

$$T_{\text{BKT}} = \frac{\pi}{2} J(T_{\text{BKT}})$$
The BKT transition temperature equals π/2 times the stiffness.
What is in the formula
T_BKTvariableBerezinskii–Kosterlitz–Thouless transition temperature — temperature kelvin
J(T_BKT)variableSuperfluid stiffness (spin-wave stiffness) evaluated at the transition temperature — superfluid stiffness joule
πconstantMathematical constant, ratio of a circle's circumference to its diameter — pi = 3.14159
t_{{bkt}}=\frac{π}{2}j(t_{{bkt}}) · 2607.08353
$$T_{\mathrm{BKT}} = \frac{\pi}{2} \rho_s(0)$$
Temperature of vortex unbinding in 2D superfluids.
What is in the formula
T_BKTvariableBKT transition temperature — temperature kelvin
ρ_svariableSuperfluid density at zero temperature — superfluid density kilogram per metre
t_{\rmbkt}=\frac{π}{8}\sqrt{\detd_s} · 2607.02267

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